Hi Merwann,
The second link is causing the confusion as the static Map API has nothing to do with the quad key. Look at the topic linked in the directly accessing tiles to see the Metadata call https://learn.microsoft.com/en-us/bingmaps/rest-services/imagery/get-imagery-metadata and in this call you ask for the URL end point of the imagery type you want to use (See the variable ImagerySet")
Sincerely,
IoTGirl